Multi-level Analysis using Mplus

In conventional regression analysis it is assumed that subjects are randomly selected and, therefore, all the variance in your variables is due solely to variation amongst individuals. However, when subjects are clustered within a group and multiple groups are sampled (e.g. students clustered within multiple classes), although some of the variance in your variables will be due to variation amongst individuals, some the variance in your variables will also be due to variation amongst the groups themselves. In such cases, multilevel analysis should be employed to account for the different levels of variation.


Multilevel analysis should be employed whenever the variance of your variables is complicated by a hierarchical sampling design. That is, whenever observations are derived from subjects nested within groups or whenever repeated measures are nested within subjects. For example, in education we may have data from students who are nested within classrooms; in business we may have data from employees who are nested within different companies; in health we may have data from patients who are nested within different hospitals. Repeated measure designs should also be analysed using multilevel analysis because the repeated observations are nested within subjects. For example, in marketing we may have repeated measures of consumers’ attitudes to a brand over the life of a marketing campaign; in epidemiology we may have repeated measures of a health outcome over the life of a drug treatment regime.


This course is designed take participants through an introductory level up to an intermediate level of multilevel analysis. That is, the course assumes that participants have had no prior experience with multilevel modeling (or have only a basis understanding) and takes participants through the basics up to an intermediate level. Although there are several programs that can be used to conduct multilevel analysis, in this course we will use the Mplus program. The course is divided into four parts:


Part 1: Introduction to multilevel data and revision of basic analytical techniques. This part of the course describes the nature of multilevel data and introduces the Mplus programming language by revising basic single-level regression models and basic single-level confirmatory factor analysis.


Part I1: Fundamentals of multilevel analysis. This part of the course introduces the fundamentals of Multilevel modeling noting the difference between the conventional (single-level) regression approach and the multilevel regression approach. The dangers of not treating nested data as multilevel data will be explored and the advantages of multilevel analysis will be described.


Part III: Investigating types of multilevel models using Mplus. This part of the course will demonstrate a range of multilevel models. The Mplus syntax required to run such models will be introduced and a thorough interpretation of the output from Mplus will be explained. Types of models will include:

  • Two-level regression models: These models investigate two-level research questions where subjects are nested within groups and explanatory (independent) variables have been measured at the subject level (Level 1) and/or the group level (Level 2). For example, in education, our outcome variable may be “reading comprehension” and we could regress this outcome on both Level 1 independent variables (e.g. the student’s verbal reasoning skills, their motivation to learn, etc.) and Level 2 independent variables (e.g. the teachers experience, the average ability of all students within the class, etc.)
  • Two-level latent growth-curve models (repeated measure designs): These models investigate change over time and enable the researcher to describe how an outcome (dependent) variable is improving or declining across a number of repeated measures. For example, in marketing we may be interested in analysing consumers’ attitudes to a brand over the life of a marketing campaign. The repeated measure (attitudes) may improve as a function of time but different marketing techniques (a time varying independent variable) may also influence the rate of improvement.
  • Two-level confirmatory factor analysis (CFA) and structural equation modeling (SEM): These models introduce latent variables into the multilevel modeling framework. In multilevel CFA models the dependent variable is a factor (rather than an observed variable). Such models may or may not contain observed explanatory variables. In multilevel SEM the independent variable(s) is/are a factor (rather than an observed variable). Such models may contain observed and/or latent dependent variables.
  • Three-level Models. These models investigate three-level research questions where either subjects are nested within sub-groups and sub-groups are nested within higher level groups or repeated measures are nested within subjects who, in turn, are nested within groups. Now, not only are the explanatory (independent) variables measured at the subject level (Level 1) and/or the sub-group level (Level 2) but they may also be measure at a third level.


Part IV: Personal Research. Finally, on the last day, participants have an opportunity to work on their own research problems with the instructor’s assistance. Therefore participants are encouraged to bring a multilevel data set and/or research problem with them.


This course will take place in a computer lab.

Level 4 - runs over 5 days

Mr Philip Holmes-Smith is the principal consultant with School Research, Evaluation and Measurements Services (SREAMS), an independent educational research consultancy business. His research, evaluation and measurement interests lie in the areas of teacher effectiveness and school improvement, accountability models and benchmarking, improving the quality of teaching, using student performance data to inform teaching, and large-scale achievement testing programs. He is an experienced teacher of social science research methods and is a regular instructor at the ACSPRI programs. He also regularly teaches Structural Equation Modeling (SEM) and Multi-Level Analysis (MLA) at various universities around Australia.

Course dates: Monday 6 July 2015 - Friday 10 July 2015
Course status: Course completed (no new applicants)
Week 2
Recommended Background: 


No prior knowledge of multilevel analysis is required nor is it assumed that participants have had experience with Mplus – the Mplus programming language will be taught as part of the course. However, it is assumed that all participants will have a thorough understanding of regression analysis and factor analysis. Furthermore, it is assumed that all participants have completed a course in Structural Equation Modeling (SEM) or have had equivalent SEM experience.


Recommended Texts: 

Muthén, L.K. and Muthén, B.O. (1998-2010). Mplus User’s Guide. Sixth Edition. Los Angeles, CA: Muthén & Muthén. Available as a download at



Snijders, Tom A.B. and Bosker, Roel J. (2012). Multilevel Analysis: An Introduction to Basic and Advanced Multilevel Modeling. (2nd Ed.). London: Sage Publications


Course fees
Non Member: 
Full time student Member: 
Winter Program 2015
Supported by: 

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